super pressure balloon non-linear structural analysis and ...american institute of aeronautics and...

American Institute of Aeronautics and Astronautics1

Super Pressure Balloon Non-linear Structural Analysis andCorrelation Using Photogrammetric Measurements

Joseph V. Welch*

ILC Dover LP, Frederica, Delaware, 19946

Shirong Wang†

TCOM LP, Columbia, Maryland, 21046

and

Joseph R. Blandino‡ and Kiley McEvoy§

James Madison University, Harrisonburg, Virginia, 22807

The structural analysis of high altitude scientific balloons is studied with the introductionof innovative experimental techniques. A bi-axial material test apparatus is investigated inorder to provide a more complete definition of fabric material elongation properties. Thisfabric test device has been under development and a recent balloon material study hasprovided an excellent opportunity to evaluate its performance. Photogrammetric 3D shapemeasurements were conducted as part of a scale model balloon inflation test.Photogrammetry provides a full characterization of the 3D deformation under load so that amore rigorous evaluation of the Lagrangian strain tensor can be made. Pulling these twoexperimental efforts together, a finite element structural analysis of the balloon inflation testis presented. Material property inputs for the model were taken from both the uni-axial andbi-axial fabric testing. The 3D photogrammerty measurements were used to make detailedcomparisons between the model response and that of the balloon experiment. The bi-axialtest device was observed to under predict the actual stiffness at the initial points of the elasticmodulus curve. At higher load states the bi-axial device provided fill direction modulusmeasurements that were in better agreement with the material stiffness observed duringballoon inflation testing. A similar evaluation of the bi-axial warp modulus measurementswas not possible with the range of loads that were measured. The increase in rigor, madepossible by the Photogrammetry data, enabled a valuable evaluation the bi-axial fabrictesting device.

NomenclatureDP = inflation load incrementEf = apparent Young’s Modulus in material fill directionEw = apparent Young’s Modulus in material warp directionEAB = Lagrangian strain tensorLT = distance between adjacent targetsR2 = variability in the response variable that is explained by regressionu = displacementx = spatial coordinates

* Lead Analytical Engineer, Engineering Directorate, AIAA Senior Member.† Senior Engineer, Engineering Department.‡ Associate Professor, Integrated Science and Technology, MSC 4310, AIAA Senior Member.§ Undergraduate Research Assistant, Integrated Science and Technology, MSC 4310.

AIAA 5th Aviation, Technology, Integration, and Operations Conference (ATIO) 26-28 September 2005, Arlington, Virginia

AIAA 2005-7447

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


X = material coordinatesx = mapping from X -> x∆LT = change in length from the baselineεf = strain in material fill directionεT = strain between target and adjacent targetsεw = strain in material warp directionνfw = Poisson’s ratio, - εw / εf due to σf applied onlyνwf = Poisson’s ratio, - εf / εw due to σw applied onlyσf = stress in material fill directionσw = stress in material warp direction

I. IntroductionECHNOLOGY endeavors of the NASA Balloon Program have focused on factors enabling increases to thecapability of scientific balloon missions. Balloon program performance goals call for 6000lb suspended loads

at 110,000 ft, resulting in volumes of 22 million cubic feet. The NASA Ultra Long Duration Balloon program wasinitiated in 1997. The pumpkin style lobed super pressure design was conceived which has continued indevelopment and test as NASA’s selection for meeting these goals.

In 2004, a project was funded to investigate an alternative to the current pumpkin style design. The AlternativeULDB concept was a spherical super pressure envelope using a traditional gore method shown in Fig. 1. Thematerial class under investigation was a lightweight woven polyester fabric. New technology components for thisproject were the implementation of innovative test methods and analytical structural modeling. A recentlyimplemented fabric Bi-axial test method was used to develop mechanical property inputs necessary for structuralanalysis. A scale model test program was undertaken, where photogrammetry was used to take detailed 3Dmeasurements for tested versus analytically predicted shape comparisons.

II. Background

A. Bi-axial Fabric TestingOne frequently used method for testing the elongation of fabric materials only pulls thin strips of fabric in one

direction. This test is known as the Uni-axial Strip Tensile Test. A draw back to the Uni-axial strip tensile test isthe transverse yarns have the tendency to be pushed out of the way as the axial yarns elongate under load.1 Thiscrimp interchange effect is shown in Fig. 2. While in use, inflatable softgoods products typically have the fabricmaterial being loaded in multiple directions, creating the need for fabric mechanical properties under bi-axial loadstates. Cruciform loading fixtures have been used in that past for bi-axial loading of fabrics, especially in the tensilestructure industry. An innovative bi-axial cruciform sample loading apparatus was designed and fabricated as partof a sponsored project for the 2002 University of Delaware Senior Design competition. This device is installed inthe Instron Laboratory at ILC Dover.

B. PhotogrammetryPhotogrammetry is an optical measurement technique that has been used to characterize the static shape of

membrane and inflatable structures.2-6 By triangulating from known camera positions to the location of identicaltargets on a series of photographs, a three dimensional model of an imaged surface can be obtained. The imagedtargets are usually circular and are either projected or physically attached to the surface of the structure. Projectedtargets have the advantage of not altering the surface of the structure, but the structure can move independently ofthe projected targets. Fixed targets add mass and local stiffness to the structure, but they move with the structure sochanges in the relative position of the targets can be used to determine the strain. Recently, photogrammetry wasused to measure bi-axial strain in an inflated cylinder with application to scientific balloons.7

C. Analytical ModelingStructural analysis of softgoods inflated structures has presented some key challenges, and several techniques

have been used in the past. A variational formulation has been used in the structural analysis of balloon shapes,including the ULDB pumpkin design.8-9 Specially developed in-house finite element analysis codes, such as theGoodyear Shell program have played important roles. Commercial finite element analysis programs have not onlybeen applied to the balloon area, but also to areas where attributes of the fabric material architecture are important.10-

T


11 In some softgoods finite element analysis cases, characteristics of the fabric material response make necessary theuse of user defined material models.12-13

Several fabric modeling difficulties typically need to be addressed in structural analysis. Models with very thinmembrane elements can often fail to reach a converged solution. The combination of orthotropic and non-linearelastic material properties presents a unique challenge for the analysis model. Material models such as multi-linearelastic from ANSYS can capture characteristics of the nonlinear material behavior, but can only be used forisotropic materials. The fabric material option in LS-DYNA can be used where both orthotropic and non-linearbehaviors need to be included.

III. Current Study

A. Bi-axial Fabric TestingMaterial property testing was conducted to determine best estimates for the material inputs required for the

structural models. In this work elastic modulus, shear modulus and Poisson’s ratio were estimated. For the scalemodel test program, 3 meter diameter test spheres were inflation tested. The test articles were constructed with alightweight polyester material with a warp yarn count of 101 and a fill yarn count of 70. The material had a 0.5 milMylar coating on one side and a finished weight of 2.38 oz/yd2. Uni-axial strip tensile testing was conducted for tensamples. Five each samples in the warp and five each in the fill direction were tested. The uni-axial data wasmeasured as a baseline for comparison with the subsequent bi-axial measurements. The uni-axial Instron testingwas conducted with preload cycling and at both 30.5 cm/min and 5.1 cm/min Instron head speeds. Test sampleextension was recorded with a 1-inch extensometer.

Bi-axial testing was conducted for two cruciform samples of the material as shown in Fig. 3. A third sample wasprepared but failed during Instron testing. In order to obtain a uniform stress distribution at the center region ofcruciform sample, leg slitting was performed on each sample. Before bi-axial tensile testing, each sample was pre-loaded in warp and fill directions ten times, respectively. The pre-loads applied were 26.3 N/cm in warp and 21.9N/cm in fill. A warp to fill load ratio of 1:1 was used for this testing due to the spherical geometry of the inflatabletest article. The design model for the bi-axial loading device is shown in Fig. 4. The bi-axial test setup is shown inFig. 5 and 6. Strain measurements were recorded using two one inch extensometers aligned with the warp and fillyarn directions. With the bi-axial test fixture, the vertical load is controlled and recorded through the Instron device.Horizontal load is applied to the sample by two pneumatic cylinders positioned by the trellis frame on linearbearings. Horizontal load is held at a constant value while the vertical loading changes. Both of the cruciformsamples were tested twice, once with varying load in the warp direction and once with varying load in the filldirection.

Shear modulus for the material was determined with an inflated cylinder torsion test. The test setup for the shearmodulus test is shown in Fig. 7. Two samples were tested. One sample had warp in axial direction and fill in hoopdirection and the other vice versa. During the test, different inflation pressures (3.45, 6.9, 10.35, and 13.8 KPa) wereapplied to each sample to see the influence of inflation pressure on fabric shear stiffness. Torque was manuallyapplied to the sample with a torque wrench and angular change of the cylindrical sample was measured.

B. PhotogrammetryFor this investigation images from four 5.0 megapixel cameras were used in the photogrammetric analysis to

measure the shape of the section of the balloon. One hundred and thirty 3.2 mm dia. retro-reflective targets wereattached to the balloon’s surface. The majority of the targets were arranged within a single gore with additionaltargets positioned to measure the balloon circumference at 90° to the gore centerline. The targets had a horizontalspacing of approximately 130 mm while the vertical spacing ranged from approximately 60 to 140 mm. Because ofthe small size of the targets and spacing, the targets added minimal mass to the balloon skin and any local stiffnesscaused by the targets was negligible. The balloon with targets attached is shown in Fig. 8. The cameras were set-upas shown in Fig. 9. The cameras were positioned in groups of two. Targets near the center of the gore were seen byall four cameras, while targets near either end of the gore were only seen by two cameras. Although it would havebeen preferable for every area of the balloon be imaged by at least 3 cameras, only a total of four cameras wereavailable for these tests. The cameras were equipped with ring flashes and wireless triggering devices. The cameratriggering was staggered with an interval of 0.1 s. This avoided the flash from one camera causing glare in anothercamera’s image. Since the balloon was stationary obtaining asynchronous images had no detrimental effect onmeasurement accuracy. An invar scale bar was used to set image scale. A second scale bar was used to asses theaccuracy of the measurements. The balloon was inflated and the pressure monitored using an electronic pressure


gage. The balloon was inflated and images collected at gage pressures from 249 Pa to 4,828 Pa. Images werecollected at every 689 Pa (0.1 psig).

C. 3 Meter Test Sphere Analytical ModelFor the scale model test program, 16 gore spheres were fabricated and tested. The test article configuration

included end caps at the pole locations. Fabric warp direction ran along the meridional direction while the fill ranalong the hoop direction. Three planes of symmetry were used to model 1/8th of the full shape. Increased stiffnesswas modeled at the seam locations by appropriately increasing thickness in these areas. The commercial finiteelement program LS-Dyna was used to analyze the inflatable structure. Using the explicit finite element codehelped to avoid some of the convergence difficulties associated with thin membrane structures. The dynamicrelaxation option in LS-Dyna was used to obtain a quasi-static solution for each pressure level. The elementformulation used was the Fully Integrated Belytschko-Tsay Membrane. There were a total of 3628 elements in themodel. The finite element model mesh is shown in Fig. 10. The initial shape was determined using thephotogrammetry measurements recorded for the lowest practical inflation pressure. A CAD model of the initialsurface shape was constructed employing the symmetry conditions assumed in the model. The nodes of the finiteelement grid were projected onto this surface to achieve an accurate match. The non-linear orthotropic fabric option(LS-Dyna MAT_034) was used. See the results section for the specific details concerning the material propertyinput data.

IV. Results

A. Bi-Axial Fabric TestingThe result of torsion cylinder testing of the two samples is shown in Fig. 11. It can be seen from the results that

the influence of inflation pressure on shear stiffness for this fabric is not significant in the tested range. Therefore, anaverage value of 0.268 GPa was used for the fabric shear modulus in the FEA. These results and all others werecalculated using an effective thickness of 0.0914 millimeter. It is assumed in the test data reduction and in theanalysis that thinning is not present.

Figure 12 shows the results of the uni-axial strip tensile testing. The data indicates an initial non-linear regionthat transitions to a extended linear region. Based on results from balloon inflation testing, the region of interest is 0to 4% in the fill direction and 0 to 2% in the warp direction. The presence of material creep at higher ballooninflation loads limited our investigation to this region.

After bi-axial testing, data reduction was completed to calculate apparent Young’s Modulus in warp & filldirections. Additionally, the two Poisson’s ratios, νfw & νwf, must be determined. Calculations were made at each ofthe different 1:1 load levels evaluated. The following system of equations was used to solve for the four unknowns:

w

wwf

f

ff EE

σνσ

ε ∆−

∆=∆ (1)

f

ffw

w

ww EE

σνσε

∆−

∆=∆ (2)

In these equations, ∆σw, ∆σf, ∆εw, and ∆εf are measured increments of stresses and strains in warp and fill directions,respectively. Figures 13 and 14 show plots of the bi-axial modulus measurements versus the load that they weremeasured at. Also included in these plots is a comparison with the uni-axial results. Figure 15 show plots of thePoisson’s ratio measurements versus load state.

The bi-axial modulus testing was seen to under predict the actual material stiffness. This result was mostnotable for the bi-axial measurements made at lowest load. The measurement error was made clear when comparedagainst the stiffer material response from the photogrammetric measurements of the inflated balloon. To investigatethe measurement errors in the bi-axial testing, the horizontal load cell data was reviewed. There were observeddifferences between the two load cells used in the horizontal line of action. These in line load cells should in theoryread the same value. Although the magnitude of the difference was as high as 6% in some cases, these differenceswere not significant. When fitting a curve to the horizontal load cell data, the R-Squared for one of the two cellswas consistently lower. One cell gave consistently reasonable fits with R-Squared between 0.90 and 0.99. The


other cell contained a great deal of scatter with R-Squared in the 0.20 to 0.90 range. Modulus results wererecalculated using only the load readings from the more consistent load cell. This exercise resulted in only smallchanges to the original modulus estimates. Although the error source was not pin pointed, the followingimprovements are suggested for the device.

1) Use higher density of load states where bi-axial measurements are taken2) Greater number of overall samples3) Improved weight relief for horizontal sample clamps4) Use regression estimates for change in horizontal force5) Replace horizontal load cells6) LVDT instrumentation to track linear bearings controlling the sample center7) Projection of laser alignment markings onto sample to ensure sample alignmentIn the discussion of the structural analysis results, simulations are presented for two cases. The first case

presents results using uni-axial data for warp and fill modulus. An evaluation of the bi-axial modulus at higher loadstates is then presented. For this second case, the uni-axial modulus results are used for the initial region and the bi-axial measurements are used for stress states higher than 15 MPa.

B. Photogrammety Results and Strain MeasurementThe pressure at 249 Pa was used as the baseline for determining the distance between targets. At this pressure

the near spherical shape of the balloon was defined, yet the skin was subjected to minimal tension. It was notpractical to obtain images of the balloon skin in an un-inflated state to obtain the true zero stress state of the balloon.At each pressure a set of three dimensional coordinates was obtained from the photogrammetric analysis. Thedistance between adjacent targets at each pressure was determined from the coordinates using,

( ) ( ) ( )222

ijijijTzzyyxxL −+−+−= (3)

and

baseline,inflated, TTTLLL −=∆ (4)

Comparing identical targets in inflated and baseline data sets the strain was obtained using,

T

T

T L

L∆=ε (5)

Because the accuracy of any photogrammetric analysis is dependent on camera placement it is necessary toassess accuracy for each project. For this study we used two invar scale bars. The first bar was 1596 mm in lengthand was used to set the scale of the images. A second 1346 mm invar bar was used to asses the overall accuracy ofthe measurement system. Table 1 compares the measured length of the bar for each data set. The data indicates thatthe all measurements fall within 0.1 mm of the Mean.

In addition to the general understanding of strain, as in equation 5, the photogrammetry data enables a moredetailed understanding of the strain state. Using the shape measurements at the minimal inflation load of 249 Paestablished the reference configuration or material coordinates X. The mapping x is used to describe the motion as

Table 1. Comparison between actual and measured scale bar lengthsPressure (gage, Pa) Actual Length (mm) Measured Length (mm)

249 1346.00 1345.82689 1346.00 1345.65

1379 1346.00 1345.712068 1346.00 1345.752758 1346.00 1345.813447 1346.00 1345.744137 1346.00 1345.674848 1346.00 1345.68

Mean 1345.73St. Dev. 0.06


pressure load is applied. A particle of material initially at position X in reference coordinates, moves to a position xin spatial coordinates. Displacement is expressed as the difference between the spatial and reference coordinates.

t),(Xx x= (6)

Xxu −= )()( tt (7)

Using indicial notation the Lagrangian strain tensor can be expressed as the following.

∂∂+

∂∂+

∂∂

∂∂=

B

A

A

B

B

i

A

iAB X

u

X

u

X

u

X

uE

21

(8)

Some Mathematica code was developed to calculate the Lagrangian strain tensor given the photogrammetry datasets. The scale bars provided for the definition of a fixed reference coordinate system. Sorts were conducted to putthe data in the structured i,j grid used for the retro targets. In the main loop, the following steps were followed foreach material coordinate.

1) Establish x,y local coordinate system using the structured i,j target grid2) Transform material and current coordinates into local system3) Calculate displacements in local coordinate frame4) Estimate partial derivatives5) Calculate strain tensor components

These results were compared with the general approach used in equation 5 and as expected the results were in veryclose agreement. An example of the resultant strain field is shown in Fig. 16. Using some vector algebra anapproximate balloon center could be estimated. This enabled displacement field plots relative to the estimatedballoon center coordinate system. Figure 17 shows an example of the displacement field plot.

C. Structural Analysis ModelStructural analysis results are presented for two cases. The first case investigates the uni-axial modulus

measurements. Analysis runs using the uni-axial modulus measurements are compared with the photogrammetryresults of the balloon inflation experiment. The second case investigates the bi-axial modulus measurements at loadstates beyond the first two measurements. So for the eight total bi-axial modulus measurement points, the thirdthrough the eighth are used in this case. Analysis runs for this case are also compared with the photogrammetryresults of the balloon inflation experiment.

As mentioned in the discussion of the material testing results, the bi-axial modulus measurements at low loadsappeared to be significantly less than the actual observed stiffness. It was expected that the bi-axial results wouldn’texactly match the uni-axial results. This difference was not expected to be very large. As shown in Figures 13 and14, the first two bi-axial measurement points deviated from the uni-axial data by as much as 50%. The density ofmeasurement points in this low load region was also insufficient. The uni-axial data showed significant moduluschange in the low load region. There were not enough data points to determine if the bi-axial measurements exhibitthe same trend. These two observations help to show that the bi-axial modulus predictions in the low load regionswere not accurate. To confirm this observation a structural analysis model was run using the as measured bi-axialmodulus predictions. When compared against the inflated balloon experiment, the difference in strain between theanalysis model and photogrammetry measurements was as high as 60%. The largest difference was observed at thelowest measured load. The difference between the model and experiment dropped as the inflation loads increased.The modulus measurements at low load were not accurate, but some further investigations were possible to evaluatethe bi-axial measurements at higher load states.

As expected, there appeared to be some level of agreement between the uni-axial tensile testing and thephotogrammetry results for the inflated balloon. Structural models were run to report these comparisons for all sixof the inflation load measurements that have been reported for the photogrammetry experiment. In this run theengineering constants for the material were taken from the following:

1) Uni-Axial Test - Ef & Ew

2) Bi-Axial Test - νfw & νwf

3) Torsion Cylinder Test – Shear modulusResults are presented in Fig. 18 through 20 for hoop and meridian strain. In these graphs the gore centerline strainsare reported at different elevations, as measured from the equator plane. The material fill direction coincided with


the hoop direction for the balloon experiment. Using strain at the equator as a reference, the model versusexperiment difference for hoop strain was between 5 and 14% for the three cases. The materials warp directioncoincided with the meridian direction for the balloon experiment. The model versus experiment difference formeridian strain was between 15 and 33% for the three cases. Using the modulus from uni-axial experiments overpredicts stiffness in both warp and fill directions. For this specific material and load condition, the warp overpredicts stiffness by a greater margin than the fill.

In order to get a general assessment of bi-axial modulus measurements at higher loading, a hybrid case wasinvestigated. In this run the engineering constants for the material were taken from the following:

1) Uni-Axial Test - Ef & Ew at loads less than 15 MPaBi-Axial Test - Ef & Ew at loads greater than 15 MPa2) Bi-Axial Test - νfw & νwf

3) Torsion Cylinder Test – Shear modulusIt was not possible to evaluate the warp direction bi-axial measurements with this case. With the warp’s higherstiffness, all the cases through 4579 Pa did not extend beyond the 15 MPa load region. With the baseline materialthickness, the 15 MPa load is equal to 137 N/cm. In the case of the fill direction, the material response extendedbeyond the 15 MPa region. This provided several points where the bi-axial fill modulus measurements could beevaluated. The load case of 1820 Pa inflation pressure was taken as a baseline. Strain increment versus loadincrement was compared with the experimental data. Figure 21 shows plots of strain increment versus elevation, asmeasured from the equator plane. The data is presented is for four delta pressure conditions of; 690, 1380, 2070,and 2760 Pa. Using the hybrid case and evaluating strain increments, the bi-axial measurements of modulus abovethe 15 MPa initial region are in good agreement with the Photogrammetry experimental measurements.

V. ConclusionMaterial stiffness values determined from uni-axial testing were stiffer than the measured balloon response due

to inflation loads. This result helps to illustrate the need for a bi-axial fabric testing device. There were mixedresults when evaluating the stiffness predictions generated using the new bi-axial testing device. The bi-axial devicewas ineffective for load regions less than 137 N/cm . Bi-axial device design changes and experimental setupimprovements have been identified to help rectify this problem. Six of the bi-axial fill modulus measurements wereused to evaluate load regions greater than 137 N/cm. These fill modulus measurements showed much betteragreement with the responses observed during balloon inflation testing. Additional evaluations of the new bi-axialdevice will be needed to validate its performance after the noted design improvements have been made.

The implementation of Photogrammetry was a critical aspect of this study allowing for a more detailed andrigorous evaluation of the bi-axial testing device. Deformation and strain are the key validation parameters forcomparing model versus experiment results for inflatable fabric products. In the balloon inflation experiment,deformation was characterized by tracking the location of the targets at each load level. With the balloondeformation characterized, material strain versus load was compared with the material stiffness predicted from bi-axial testing. These strains, calculated using photogrammetry, provided a much more detailed data set for model vs.experiment correlation.

AcknowledgmentsJoseph V. Welch thanks the University of Delaware Mechanical Engineering graduates who designed and

fabricated the bi-axial device as part of their Senior Design competition. These individuals are Dan Gleeson, DavidForney, and Jonathan Watts.

References1Poturi, P., Perez Ciurezu, D.A., Ramgulam R., “Measurement of meso-scale deformations for modeling textile composites,”

Proceedings of the 2nd International Conference on Composites Testing and Model Identification CompTest 2004, University ofBristol, Bristol, U.K., 2004.

2Rand, J.L., “Balloon Film Strain Measurement,” Advances in Space Research, Vol. 3, No. 6, 1983, pp. 45-48, (BT-2470.06).3Pappa, R.S., Geirsch, L.R., and Quagliaroli, J.M., “Photogrammetry of a 5-m Inflatable Space Antenna with Consumer-

Grade Digital Cameras,” Experimental Techniques, July/August, 2001, pp. 21-29.


4Jones T.W. and Pappa, R.S., “Dot Projection Photogrammetric Technique for Shape Measurements of Aerospace TestArticles,” Proceedings of the 40th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2002-532, Reno, NV, 2002.

5Blandino, J.R., Johnston, J.D., and Dharamsi, U.K., “Corner Wrinkling of a Square Kapton Membrane,” Journal ofSpacecraft and Rockets, Vol. 39, No. 5, Sept-Oct, 2002, pp. 717-724.

6Blandino, J.R., Johnston, J.D., Miles, J.J., and Dharamsi, U.K., “The Effect of Asymmetric Mechanical and ThermalLoading on Membrane Wrinkling,” Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics andMaterials Conference, AIAA-2002-1371, Denver, Colorado, 2002.

7Blandino, J.R., Sterling, J., Baginski, F., Steadman, E., Black, J.T., and Pappa, R.S., “Optical Strain Measurement of anInflated Cylinder using Photogrammetry with Application to Scientific Balloons,” Proceedings of the 45thAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-2004-1500, Palm Springs,California, 2004.

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9Baginski F., Collier W., “A Mathematical Model for the Strained Shape of a Large Scientific Balloon at Float Altitude,”ASME Journal of Applied Mechanics, Vol. 67, No. 1, 2000, 6-16.

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11Cavallaro P.V., Sadegh A.M., Quigley, C.J., Johnson A.R., “Effects of Coupled Biaxial Tension and Shear Stresses onDecrimping Behavior in Pressurized Woven Fabrics,” Naval Undersea Warfare Center, Technical Report 11,571, Newport,Rhode Island, October 2004.

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Figure 2. Uni-axial strip tensile movement of yarns.

2 - Gore

3 - EndCap

Figure 1. Design concept proposed for Alternate ULDB.


Red lines are cut linesGreen lines are marked

Black dashed lines represent the stitch rows

0.5”

8” 2”

Marks for MountingExtensometers

Figure 3. Cruciform fabric test sample.

Figure 4. Bi-axial load apparatus CAD model.


Figure 5. Bi-axial test device installed in Instron.

Figure 6. Cruciform sample loading.


Pressure DrumCylindricalFabric Sample

Torque Wrench

Angle Reading device

Figure7. Inflated cylinder torsion test.

Figure 8. Balloon with retro-reflective targets.


Figure 9. Camera positions with respect to the balloon.

Figure 10. Finite element model mesh.


0

10

20

30

40

50

60

70

80

0 0.01 0.02 0.03 0.04Strain

Str

ess,

MP

a

Warp

Fill

Figure 12. Uni-axial stress-strain curve.

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

Inflation Pressure, KPa

Mea

sure

dS

hea

rM

od

ulu

s,G

Pa

Sample 1 (Warp in CylinderAxial Direction)

Sample 2 (Fill in Cylinder AxialDirection)

Figure 11. Shear modulus measurements.


1

1.5

2

2.5

3

3.5

0 10 20 30 40 50Stress, MPa

Ap

par

ent

Mo

du

lus,

GP

a

Uni-Axial 5 Sample Avg.

Bi-Axial Sample 2

Bi-Axial Sample 3

Uni-Axial Poly. Regression

Figure 14. Warp direction modulus measurements.

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50Stress, MPa

Ap

par

ent

Mo

du

lus,

GP

aUni-Axial 5 Sample Avg.

B--Axial Sample 2

B-Axial Sample 3

Uni-Axial Poly. Regression

Figure 13. Fill direction modulus measurements.


0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Stress, MPa

Po

isso

n's

Rat

io

PRfw Sample3

PRwf Sample3

PRfw Sample2

PRwf Sample 2

Figure 15. Measured Poisson’s Ratio.

E11

0.0210.020.0190.0180.0170.0160.0150.0140.0130.0120.0110.010.0090.008

3890 Pa Inflation Load

Figure 16. Hoop direction strain contour plot (experiment)


0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

-150 -120 -90 -60 -30 0 30 60 90 120 150

Elevation From Equator cm

Str

ain

Hoop Strain Model

Meridian Strain Model

Hoop Strain Experiment

Meridian Strain Experiment

Figure 18. Hoop and meridian strain along gore centerline at 1131 Pa.

X

600800

10001200

1400Y

-300 -200 -100 0 100 200 300

Z

-1500

-1000

-500

0

500

1000

1500

UMAG

424038363432302826242220181614121086

4579 Pa Inflation PressureDisplacement Magnitude in mm

Figure 17. Displacement magnitude contour plot (experiment)


0

0.002

0.004

0.006

0.008

0.01

0.012

-150 -120 -90 -60 -30 0 30 60 90 120 150


Str

ain


Hoop Strain Model


Merdian Strain Model


0

0.005

0.01

0.015

0.02

0.025

-150 -120 -90 -60 -30 0 30 60 90 120 150


Str

ain


Hoop Strain Model


Meridian Strain Model



0.000

0.005

0.010

0.015

0.020

0.025

-150 -120 -90 -60 -30 0 30 60 90 120 150


Str

ain

Incr

emen

t

DP=690 Pa Experiment




DP=690 Pa Model

DP=1380 Pa Model

DP=2070 Pa Model

DP=2760 Pa Model

Figure 21. Strain increment using bi-axial modulus measurements

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